OCR C2 2010 January — Question 3 6 marks

Exam BoardOCR
ModuleC2 (Core Mathematics 2)
Year2010
SessionJanuary
Marks6
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicBinomial Theorem (positive integer n)
TypeSubstitution into binomial expansion
DifficultyModerate -0.8 This is a straightforward binomial expansion question requiring routine application of the binomial theorem formula, followed by a simple substitution. Part (i) is mechanical calculation with no problem-solving, and part (ii) requires only recognizing that substituting x = w²/4 means the x³ term becomes the w⁶ term. Both parts are below average difficulty for A-level, being standard textbook exercises with clear methods.
Spec1.04a Binomial expansion: (a+b)^n for positive integer n1.04b Binomial probabilities: link to binomial expansion

3
  1. Find and simplify the first four terms in the expansion of \(( 2 - x ) ^ { 7 }\) in ascending powers of \(x\).
  2. Hence find the coefficient of \(w ^ { 6 }\) in the expansion of \(\left( 2 - \frac { 1 } { 4 } w ^ { 2 } \right) ^ { 7 }\).

3 (i) Find and simplify the first four terms in the expansion of $( 2 - x ) ^ { 7 }$ in ascending powers of $x$.\\
(ii) Hence find the coefficient of $w ^ { 6 }$ in the expansion of $\left( 2 - \frac { 1 } { 4 } w ^ { 2 } \right) ^ { 7 }$.

\hfill \mbox{\textit{OCR C2 2010 Q3 [6]}}